On the effect of packet acknowledgment on the stability and performance of networked control systems

This work concerns discrete-time Linear Quadratic Gaussian (LQG) optimal control of a remote plant that communicates with the control unit by means of a packets dropping channel. Namely, the output measurements are sent to the control unit through an unreliable network and the actions decided by the control unit are sent to the plant actuator via the same network. Sensor and control packets may be randomly lost according to a Bernoulli process. In this work we focus on the importance of acknowledgments in the communication between the control unit and the actuators. In the literature two extreme cases have been considered: either guaranteed acknowledgment or complete lack of it. Although very common in practice, the case where the acknowledgment packets can be lost has not been dealt with a sufficient level of detail. In this work we focus on such a case by assuming that also the acknowledgment packets can be lost according to a Bernoulli process. We can show how the partial loss of acknowledgements yields a non classical information pattern [1], making the optimal control law a nonlinear function of the information set. For the special case each observation packet contains the complete state information, we can prove linearity of the optimal controller. Furthermore, we can compute the control law in closed form and show that the stability range increases monotonically with the arrival rate of the acknowledgement packets.